如何提取这个多态递归函数

Question

我正在用GHC7.8做一些非常有趣的事情，但遇到了一些问题。我有以下内容：

mkResultF :: Eq k => Query kvs ('KV k v) -> k -> ResultF (Reverse kvs) (Maybe v)
mkResultF Here key = ResultComp (pure . lookup key)
mkResultF q@(There p) key =
  case mkResultF p key of
    ResultFId a -> pure a
    ResultComp c ->
      ResultComp $ foo ->
       case c foo of
         ResultFId a -> pure a
         ResultComp c ->
           ResultComp $ foo ->
            case c foo of
              ResultFId a -> pure a

显然，这里有一些东西需要抽象，但我不太清楚如何做到这一点

mkResultF :: Eq k => Query kvs ('KV k v) -> k -> ResultF (Reverse kvs) (Maybe v)
mkResultF Here key = ResultComp (pure . lookup key)
mkResultF q@(There p) key = magic (mkResultF p key)
magic :: ResultF (Reverse kvs) (Maybe v) -> ResultF (Reverse kvs ++ '[('KV x y)]) (Maybe v)
magic (ResultFId a) = pure a
magic (ResultComp c) = ResultComp (foo -> magic (c foo))

这感觉像是一个"显而易见"的解决方案，但它没有键入检查：

Could not deduce (kvs2 ~ Reverse kvs0)
from the context (Reverse kvs ~ ('KV k v1 : kvs2))
  bound by a pattern with constructor
             ResultComp :: forall a k v (kvs :: [KV * *]).
                           ([(k, v)] -> ResultF kvs a) -> ResultF ('KV k v : kvs) a,
           in an equation for `magic'
  at query-kv.hs:202:8-19
  `kvs2' is a rigid type variable bound by
         a pattern with constructor
           ResultComp :: forall a k v (kvs :: [KV * *]).
                         ([(k, v)] -> ResultF kvs a) -> ResultF ('KV k v : kvs) a,
         in an equation for `magic'
         at query-kv.hs:202:8
Expected type: ResultF (Reverse kvs0) (Maybe v)
  Actual type: ResultF kvs2 (Maybe v)
Relevant bindings include
  c :: [(k, v1)] -> ResultF kvs2 (Maybe v)
    (bound at query-kv.hs:202:19)
In the first argument of `magic', namely `(c foo)'
In the expression: magic (c foo)

我真的很纠结。包含起始代码的完整代码列表可以在此处找到：https://gist.github.com/ocharles/669758b762b426a3f930

Answer 1

为什么启用AllowAmbiguousTypes？这几乎从来都不是个好主意。如果没有扩展，你会得到一个更好的错误消息：

Couldn't match type ‘Reverse kvs0’ with ‘Reverse kvs’
NB: ‘Reverse’ is a type function, and may not be injective
The type variable ‘kvs0’ is ambiguous
Expected type: ResultF (Reverse kvs) (Maybe v)
               -> ResultF (Reverse kvs ++ '['KV x y]) (Maybe v)
  Actual type: ResultF (Reverse kvs0) (Maybe v)
               -> ResultF (Reverse kvs0 ++ '['KV x0 y0]) (Maybe v)
In the ambiguity check for:
  forall (kvs :: [KV * *]) v x y.
  ResultF (Reverse kvs) (Maybe v)
  -> ResultF (Reverse kvs ++ '['KV x y]) (Maybe v)
To defer the ambiguity check to use sites, enable AllowAmbiguousTypes
In the type signature for ‘magic’:
  magic :: ResultF (Reverse kvs) (Maybe v)
           -> ResultF (Reverse kvs ++ '[KV x y]) (Maybe v)

问题确实存在于magic的类型签名中，其中有

magic :: ResultF (Reverse kvs) (Maybe v)
      -> ResultF (Reverse kvs ++ '[('KV x y)]) (Maybe v)

所有变量kvs、x和y仅作为Reverse和++的自变量出现，这两个变量是类型族，不需要是内射的。这种情况总是令人怀疑。

最简单的解决方法是添加代理。以下是为我编译的代码：

mkResultF :: forall k v kvs. Eq k
           => Query kvs ('KV k v) -> k -> ResultF (Reverse kvs) (Maybe v)
mkResultF Here key = ResultComp (pure . lookup key)
mkResultF (There p) key = magic (Proxy :: Proxy kvs) (mkResultF p key)
magic :: Proxy ('KV x y ': kvs)
      -> ResultF (Reverse kvs) (Maybe v)
      -> ResultF (Reverse ('KV x y ': kvs)) (Maybe v)
magic _ r =
  case r of
    ResultFId a -> pure a
    ResultComp c ->
      ResultComp $ foo ->
       case c foo of
         ResultFId a -> pure a
         ResultComp c ->
           ResultComp $ foo ->
            case c foo of
              ResultFId a -> pure a

---

编辑

我又看了一遍，这里有一个版本使用了您对magic(作为magic2(的定义。它仍然不是很优雅，但它有望成为概念的证明：

mkResultF :: forall k v kvs. Eq k
           => Query kvs ('KV k v) -> k -> ResultF (Reverse kvs) (Maybe v)
mkResultF Here      key = ResultComp (pure . lookup key)
mkResultF (There p) key = magic1 (Proxy :: Proxy kvs) (mkResultF p key)
magic1 :: forall x y kvs v. Proxy ('KV x y ': kvs)
       -> ResultF (Reverse kvs) (Maybe v)
       -> ResultF (Reverse ('KV x y ': kvs)) (Maybe v)
magic1 _ = magic2 (Proxy :: Proxy ('KV x y)) (Proxy :: Proxy (Reverse kvs))
magic2 :: Proxy ('KV x y) -> Proxy kvs
       -> ResultF kvs (Maybe v)
       -> ResultF (kvs ++ '[('KV x y)]) (Maybe v)
magic2 _ _ (ResultFId a) = pure a
magic2 p _ (ResultComp (c :: ([(k, v')] -> ResultF kvs' (Maybe v))))
  = ResultComp ( foo -> magic2 p (Proxy :: Proxy kvs') (c foo))